The bisector AM is drawn in an isosceles triangle ABC with base AC. Find the segments BM

The bisector AM is drawn in an isosceles triangle ABC with base AC. Find the segments BM and CM if AB = 12 cm and AC = 8 cm

Since the triangle ABC is isosceles, then BC = AB = 12 cm.

Let the length of the segment BM = X cm, then the length of the segment CM = (12 – X) cm.

AM is the bisector of the angle BAC, then, by the property of the bisector of the angle:

AB / BM = AC / CM.

12 / X = 8 / (12 – X).

8 * X = 144 – 12 * X.

20 * X = 144.

X = BM = 144/20 = 7.2 cm.

Then CM = BC – BM = 12 – 7.2 = 4.8 cm.

Answer: The length of the segment BM is 7.2 cm, CM is 4.8 cm.